November 25, 2016, 2 pm, PhD Defense Swan Rocher (Graphik)
November 25, 2016, 2 pm, Seminar Room, Building 4, PhD Defense Swan Rocher (Graphik)
Title: Querying Existential Rule Knowledge Bases: Decidability and Complexity
Abstract: In this thesis we investigate the issue of querying knowledge bases composed of data and general background knowledge, called an ontology. Ontological knowledge can be represented under different formalisms and we consider here a fragment of first-order logic called existential rules (also known as tuple-generating dependencies and Datalog+/-). The fundamental entailment problem at the core of this thesis asks if a conjunctive query is entailed by an existential rule knowledge base. General existential rules are highly expressive, however at the cost of undecidability. Various restrictions on sets of rules have been proposed to regain the decidability of the entailment problem. Our specific contribution is two-fold. First, we propose a new tool that allows to unify and extend most of the known existential rule classes that rely on acyclicity conditions to tame infinite forward chaining, without increasing the complexity of the acyclicity recognition. Second, we study the compatibility of known decidable rule classes with a frequently required modeling construct, namely transitivity of binary relations. We help clarifying the picture of negative and positive results on this question, and provide a technique to safely combine transitivity with one of the simplest, yet useful, decidable rule classes, namely linear rules.